What is the general solution for 144^2=43.27^2+72^2-2*43.27*72*cos(x) ?

The general solution for 144^2=43.27^2+72^2-2*43.27*72*cos(x) is No Solution for x\in\mathbb{R}

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144^2=43.27^2+72^2-243.2772*cos(x)

14 4^{2} = 43.2 7^{2} + 7 2^{2} - 2 \cdot 43.27 \cdot 72 \cdot cos (x)

No Solution for x \in R

Solution steps

14 4^{2} = 43.2 7^{2} + 7 2^{2} - 2 \cdot 43.27 \cdot 72 cos (x)

Switch sides

43.2 7^{2} + 7 2^{2} - 2 \cdot 43.27 \cdot 72 cos (x) = 14 4^{2}

Multiply the numbers:

2 \cdot 43.27 \cdot 72 = 6230.88

43.2 7^{2} + 7 2^{2} - 6230.88 cos (x) = 14 4^{2}

43.2 7^{2} = 1872.2929

1872.2929 + 7 2^{2} - 6230.88 cos (x) = 14 4^{2}

7 2^{2} = 5184

1872.2929 + 5184 - 6230.88 cos (x) = 14 4^{2}

Add the numbers:

1872.2929 + 5184 = 7056.2929

- 6230.88 cos (x) + 7056.2929 = 14 4^{2}

14 4^{2} = 20736

- 6230.88 cos (x) + 7056.2929 = 20736

Move

7056.2929

to the right side

- 6230.88 cos (x) + 7056.2929 = 20736

Subtract

7056.2929

from both sides

- 6230.88 cos (x) + 7056.2929 - 7056.2929 = 20736 - 7056.2929

Simplify

- 6230.88 cos (x) = 13679.7071

- 6230.88 cos (x) = 13679.7071

Divide both sides by

- 6230.88

- 6230.88 cos (x) = 13679.7071

Divide both sides by

- 6230.88

\frac{- 6230.88 cos ( x )}{- 6230.88} = \frac{13679.7071}{- 6230.88}

Simplify

cos (x) = - \frac{13679.7071}{6230.88}

cos (x) = - \frac{13679.7071}{6230.88}

- 1 \leq cos (x) \leq 1

No Solution for x \in R

What is the general solution for 144^2=43.27^2+72^2-2*43.27*72*cos(x) ?
The general solution for 144^2=43.27^2+72^2-2*43.27*72*cos(x) is No Solution for x\in\mathbb{R}